Spatial representation of symbolic sequences through iterative function systems

• Main Author: Tino, Peter
• Format: Others
• Language: en
• Published: SFB Adaptive Information Systems and Modelling in Economics and Management Science, WU Vienna University of Economics and Business 1998
• Subjects: Sequenz / Graphische Darstellung / Iteration
• Online Access: http://epub.wu.ac.at/926/1/document.pdf

Jeffrey proposed a graphic representation of DNA sequences using Barnsley's iterative function systems. In spite of further developments in this direction (Oliver et. al, 1993), (Roman-Roldan et. al, 1994), (Li, 1997), the proposed graphic representation of DNA sequences has been lacking a rigorous connection between its spatial scaling characteristics and the statistical characteristics of the DNA sequences themselves. We 1) generalize Jeffrey's graphic representation to accommodate (possibly infinite) sequences over an arbitrary finite number of symbols, 2) establish a direct correspondence between the statistical characterization of symbolic sequences via Renyi entropy spectra and the multifractal characteristics (Renyi generalized dimensions) of the sequences' spatial representations, 3) show that for general symbolic dynamical systems, the multifractal fH-spectra in the sequence space coincide with the fH-spectra on spatial sequence representations. (author's abstract) === Series: Working Papers SFB "Adaptive Information Systems and Modelling in Economics and Management Science"